Serializability of Transactions and Automatic (Number) Generators

Modern DBMS usually have one or more ways of automatically generating values during a transaction - Oracle (and most other DBMS) have SEQUENCE types; Informix has the SERIAL type; other DBMS have other similar constructs.

In general, the values automatically generated during a transaction are not generated again, even if the original transaction is rolled back. Further, there is nothing to stop a pair of transactions from alternately generating new values - V(n) to TxA, V(n+1) to TxB, V(n+2) to TxA, V(n+3) to TxB, and so on.

Does this mean that such transactions are inherently non-serializable, or does it mean that the specific values generated by a transaction are not material for the discussion of equivalence of executions?

If TxA were executed before TxB, it would obtain the values V(n) and V(n+1) -- rather than V(n) and V(n+2) as shown above -- but for all practical purposes, the results are equivalent: two new unique values unused by any other transaction were generated and the specific values are immaterial.

Any thoughts?

-- 
Jonathan Leffler                   #include <disclaimer.h>
Email: jleffler_at_earthlink.net, jleffler_at_us.ibm.com
Guardian of DBD::Informix v2003.04 -- http://dbi.perl.org/